Resolution of the Yang-Mills Mass Gap Problem via Srinivas Bounded Mathematics

We demonstrate that the Yang-Mills mass gap problem—one of the seven Clay Millennium Prize Problems—admits a natural resolution within the framework of Srinivas Bounded Mathematics (SBM). By applying Axiom 1 of SBM (Prohibition of Infinite Subdivision), which establishes that all spatial and momentum scales must satisfy r ≥ ε_SBM > 0 for any finite positive bound, we show that: (1) loop integrals acquire natural ultraviolet cutoffs, rendering all quantum corrections finite; (2) the impossibility of infinite momentum subdivision prevents the accumulation of infinitely many massless modes required for Δ = 0; (3) the mass gap Δ > 0 emerges as a structural necessity rather than a dynamical accident. The resolution holds universally for any finite positive ε_SBM > 0—the proof depends only on finiteness, not on specific value. This work provides rigorous mathematical foundation for what lattice QCD achieves computationally, aligns with the Wightman axioms, and ensures Osterwalder-Schrader positivity via bounded operators.